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We revisit the SICA (Susceptible-Infectious-Chronic-AIDS) mathematical model for transmission dynamics of the human immunodeficiency virus (HIV) with varying population size in a homogeneously mixing population. We consider SICA models…
Respondent-Driven Sampling (RDS) is a variant of link-tracing sampling techniques that aim to recruit hard-to-reach populations by leveraging individuals' social relationships. As such, an RDS sample has a graphical component which…
In this work we introduce a differential equation model with time-delay that describes the three-stage dynamics and the two time scales observed in HIV infection. Assuming that the virus has high mutation and rapid reproduction rates that…
The precise mechanism that causes HIV infection to progress to AIDS is still unknown. This paper presents a mathematical model which is able to predict the entire trajectory of the HIV/AIDS dynamics, then a possible explanation for this…
Multi-parameter evidence synthesis (MPES) is receiving growing attention from the epidemiological community as a coherent and flexible analytical framework to accommodate a disparate body of evidence available to inform disease incidence…
Missing data is a recurrent issue in epidemiology where the infection process may be partially observed. Approximate Bayesian Computation, an alternative to data imputation methods such as Markov Chain Monte Carlo integration, is proposed…
Estimating the prevalence of a medical condition, or the proportion of the population in which it occurs, is a fundamental problem in healthcare and public health. Accurate estimates of the relative prevalence across groups -- capturing,…
In this paper, we propose a Spatial Robust Mixture Regression model to investigate the relationship between a response variable and a set of explanatory variables over the spatial domain, assuming that the relationships may exhibit complex…
Frequently, empirical studies are plagued with missing data. When the data are missing not at random, the parameter of interest is not identifiable in general. Without additional assumptions, we can derive bounds of the parameters of…
The sampling frame in most social science surveys excludes members of certain groups, known as hard-to-reach groups. These groups, or subpopulations, may be difficult to access (the homeless, e.g.), camouflaged by stigma (individuals with…
We present a new analysis of relationships between disease incidence and the prevalence of an experimentally defined state of `recent infection'. This leads to a clean separation between biological parameters (properties of disease…
In low- and middle-income countries, household surveys are the most reliable data source to examine health and demographic indicators at the subnational level, an exercise in small area estimation. Model-based unit-level models are favored…
In low-resource settings, prevalence mapping relies on empirical prevalence data from a finite, often spatially sparse, set of surveys of communities within the region of interest, possibly supplemented by remotely sensed images that can…
We study the influence of the rate of the attainment of herd immunity (HI), in the absence of an approved vaccine, on the vulnerable population. We essentially ask the question: how hard the evolution towards the desired herd immunity could…
This article is concerned with a nonlocal dispersal susceptible-infected-susceptible (SIS) epidemic model with Neumann boundary condition, where the rates of disease transmission and recovery are assumed to be spatially heterogeneous and…
Respondent-Driven Sampling is a method to sample hard-to-reach human populations by link-tracing over their social networks. Beginning with a convenience sample, each person sampled is given a small number of uniquely identified coupons to…
This work is concerned with the estimation of hard-to-reach population sizes using a single respondent-driven sampling (RDS) survey, a variant of chain-referral sampling that leverages social relationships to reach members of a hidden…
We consider a spatially-heterogeneous generalization of a well-established model for the dynamics of the Human Immunodeficiency Virus-type 1 (HIV) within a susceptible host. The model consists of a nonlinear system of three coupled…
Recent work has focused attention on statistical inference for the population distribution of the number of sexual partners based on survey data. The characteristics of these distributions are of interest as components of mathematical…
An adequate near-optimal control problem for a stochastic SICA (Susceptible-Infected-Chronic-AIDS) compartmental epidemic model for HIV transmission with imprecise parameters is formulated and investigated. We prove some estimates for the…